Measurement and Simulation of the Nonlocal Dispersion Tensor in Porous Media

Nuclear Magnetic Resonance (NMR) techniques have been used extensively to characterise dispersion and diffusion in porous media. The completely non-invasive nature of the measurements and the ability to measure opaque samples provide the makings for an excellent tool. Detailed understanding of the microstructure of porous media leads to the ability to model and predict macroscopic effects such as ground water flow, oil extraction, blood perfusion and enable understanding of industrial catalytic reactors. The range of properties that NMR is capable of measuring is extensive but one particular quantity, the nonlocal dispersion tensor has long been identified as an ideal way to characterise dispersive effects at short time and length scales. The nonlocal dispersion tensor is a quantity that is included in theory proposed by Koch and Brady (1987) to explain non-Fickian dispersive behaviour. Demonstrated here is, for the first time, a method to measure the tensor. Details of the newly developed NMR pulse sequence and the post processing technique required to extract the nonlocal dispersion tensor are given. Successful measurements have been undertaken on model systems such as capillary flow and Couette flow. This enabled direct comparison with analytically calculated quantities and excellent agreement is found, thus verifying the methodology. A complete set of nonlocal dispersion components has been identified and measured in a model porous medium, in this case a random beadpack of monosized spheres. The new measurements provide the ability to infer and characterise the nature of fluid correlations, particularly at short length scales. In parallel, a simulation suite based on a lattice Boltzmann calculation (implemented by a co-worker Dr Andrew Jackson), has been used to independently generate the same nonlocal components as measured. The simulations have also been used to guide the design of further NMR experiments, to further investigate aspects of the new parameter space that the nonlocal dispersion tensor provides and to explore parts of the parameter space that are inaccessible by NMR. Finally, the methodology was adapted to enable nonlocal dispersion measurements on a 'real' porous medium, a Bentheimer sandstone.